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A ray of light passing from air through an equilateral glass prism undergoes minimum deviation when the angle of incidence `(3)/(4) of the angle of prism .Calculate the speed of light in the prism.

Text Solution

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Here, refracting angle `(A) = 60^(@)`
We know, minimum deviation `(delta_(m)) = 2i_(1) - A`
`therefore " " delta_(m) = 2 xx (3)/(4) A - A ["given", i_(1) = (3)/(4)A]`
`= (A)/(2) = 30^(@)`
`therefore "Refractive index of the prism",`
`mu = (sin""(A + delta_(m))/(2))/(sin""(A)/(2)) = (sin45^(@))/(sin30^(@)) = (1)/(sqrt(2)) xx 2 = sqrt(2)`
Also `mu = (c)/(v) [v = "velocity of light in the prism"]`
`therefore " " v = (c)/(mu) = (2.998 xx 10^(8))/sqrt(2) = 2.12 xx 10^(8) m*s^(-1)`
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